Answer
$(4,3),(4,-3),(-5,0)$
Work Step by Step
$x^{2}+y^{2} =25$ Equation $(1)$
$x=y^{2}-5$ Equation $(2)$
From Equation $(2)$
$y^{2}=x+5$ Equation $(3)$
Substituting $y^{2}=x+5$ in Equation $(1)$
$x^{2}+y^{2} =25$
$x^{2}+x+5 =25$
$x^{2}+x+5 -25=0$
$x^{2}+x-20=0$
By factoring,
$(x-4)(x+5)=0$
$x=4$ or $x=-5$
Substitute $x$ values in Equation $(3)$ to get $y$
Let $x=4$
$y^{2}=x+5$
$y^{2}=4+5$
$y^{2}=9$
$y=±3$
$y=3$ or $y=-3$
Let $x=-5$
$y^{2}=x+5$
$y^{2}=-5+5$
$y^{2}=0$
$y=0$
$(4,3),(4,-3),(-5,0)$ satisfy the given equations. The solutions are $(4,3),(4,-3),(-5,0)$
